Since there is no direct connectivity from New Delhi to Nuwara Eliya, you have to first fly to Colombo. There are several direct and connecting flights from New Delhi's Indira Gandhi International Airport to Bandaranaike International Airport in Colombo.
Train: You can reach Nuwara Eliya from Nanu Oya which falls on the Colombo-Kandy route. A second class ticket from Colombo costs about ₹100. Once you get off at the Nanu Oya station you can hire a cab or take a bus to Nuwara Eliya. The journey takes a total of 5-6 hours.
Road: You can also jump abroad a local bus from Colombo to Nuwara Eliya (which may take longer, as buses are usually slower) or hire a private cab. The travel time is around 5 to 5.5 hours.
Since Nuwara Eliya is a small town most places are within close proximity. You can easily hire a tuk-tuk to sight see and get around . A ride may cost you anywhere between ₹200 to ₹600 - it essentially depends on where you are headed. The rates are usually higher at night.
Flight from New Delhi to Colombo: ₹16,000
One-way ticket on local transport: ₹250
Taxi starting tariff: ₹50
Hotel stay in Nuwara Eliya: ₹3,000
A meal: ₹800 approx. (meal for 2 in a mid-range restaurant)